Backtracking. Backtracking. Backtracking. Backtracking. Backtracking. Backtracking. Functional & Logic Programming - Backtracking October, 01

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1 Functional & Logic Programming - October, 01 already seen how to control execution ordering the clauses and goals can affect the speed of execution and the order of evaluation of the clauses now going to look at controlling backtracking use of a facility called the cut also look at negation as failure October, 01 - Damien Costello 1 Prolog automatically backtracks if necessary useful concept relieves the programming responsibility however, when uncontrolled can cause inefficiencies controlled using the cut normally, if a goal fails, Prolog backtracks and tries other alternatives what about a goal failing with initial fail of 2 < 0 mutually exclusive rules also cause inefficiencies October, 01 - Damien Costello 2 Cut definition call the parent goal the goal that matched the head of the clause containing the cut. When the cut is encountered as a goal, it succeeds immediately, but it commits the system to all choices made between the time the parent goal was invoked and the time the cut was encountered. All remaining alternatives between the parent goals and the cut are ignored. October, 01 - Damien Costello 3 place the cut the same as a subgoal in the body of a rule when processing comes across the cut cut immediately succeeds next subgoal (if there is one) is called once a cut has been passed, can t backtrack to subgoals before the cut in the clause being processed other predicates defining the predicate currently in process (the predicate containing the cut). October, 01 - Damien Costello 4 two main uses of the cut know in advance that certain possibilities will never give rise to meaningful solutions waste of time and storage space to look for alternate solutions use a cut in this situation, resulting program will run quicker and use less memory. This is called a green cut. when the logic of a program demands the cut to prevent consideration of alternate subgoals. This is a red cut. October, 01 - Damien Costello 5 prevent backtracking to previous subgoal in rule r1 :- a, b,!, c. satisfied with the first solution it finds to the subgoals a and b can find multiple solutions to the call to c through backtracking can t backtrack across the cut to find an alternate solution to the calls a or b can t backtrack to another clause defining r1 October, 01 - Damien Costello 6 Damien Costello, Dept of Computing & Maths, GMIT 1

2 Functional & Logic Programming - October, 01 PREDICATES buy_car(symbol,symbol) nondeterm car(symbol,symbol,integer) colors(symbol,symbol) CLAUSES buy_car(model,color):- car(model,color,price), colors(color,sexy),!, Price < car(maserati,green,25000). car(corvette,black,24000). car(corvette,red,26000). car(porsche,red,24000). colors(red,sexy). colors(black,mean). colors(green,preppy). given the goal buy_car(corvette, Y) find a Corvette with a sexy color and a price that's ostensibly affordable the cut in the buy_car rule means that since there is only one Corvette with a sexy color in the database, if its price is too high there's no need to search for another car what happens on execution October, 01 - Damien Costello 7 October, 01 - Damien Costello 8 call car, the first subgoal to the buy_car predicate test on the first car, the Maserati, which fails then test the next car clauses and finds a match binding the variable Color with the value black proceed to the next call, test if car chosen has a sexy color black is not a sexy color in the program, so the test fails October, 01 - Damien Costello 9 backtrack to the call to car once again look for a Corvette to meet the criteria find a match and again tests the color this time the color is sexy proceed to the next subgoal: the cut immediately succeeds effectively "freezes into place" the variable bindings previously made in this clause October, 01 - Damien Costello 10 proceed to the next (and final) subgoal in the rule: the comparison Price < this test fails attempts to backtrack in order to find another car to test cut prevents backtracking there is no other way to solve the final subgoal the goal terminates in failure. October, 01 - Damien Costello 11 can also use the cut to define a switch like set of rules r(1):-!, a, b, c. r(2):-!, d. r(3):-!, c. r(_):- write("this is a catchall clause."). using the cut makes the predicate r deterministic r is called with a single integer argument call is r(1) search for a match to the call October, 01 - Damien Costello 12 Damien Costello, Dept of Computing & Maths, GMIT 2

3 Functional & Logic Programming - October, 01 find one with the first clause defining r places a backtracking point next to this clause process the body of the rule passing the cut eliminates the possibility of backtracking to another r clause increasing the run-time efficiency it also ensures that the error-trapping clause is executed only if none of the other conditions match the call to r October, 01 - Damien Costello 13 Negation as failure Mary likes all animals except snakes in prolog Mary likes any X if X is an animal likes(mary, X) :- animal(x). What about the snakes introducing the fail predicate add the rule likes(mary,x) :- snake(x),!, fail. Cut prevents backtracking, fail will cause failure October, 01 - Damien Costello 14 Negation as Failure now have two rules likes(mary, X) :- snake(x),!, fail. likes(mary, X) :- animal(x). First rule takes care of snakes cut prevents backtracking to evaluate other rules can write more compactly as likes(mary, X) :- snake(x),!, fail ; animal(x)., binds stronger than ; October, 01 - Damien Costello 15 follows from negation consider the definition different(x,y) :- X=Y,!, fail ; true X Y different if they do not match true always succeeds indicates the usefulness of a not not is defined as not(p) :- P,!, fail ; true. October, 01 - Damien Costello 16 can change Mary s likings to likes(mary, X) :- animal(x), not snake(x). the not predicate succeeds when the subgoal can't be proven true this results in a situation that prevents unbound variables from being bound within a not when a subgoal with free variables is called from within not error: Free variables not allowed in 'not' or 'retractall October, 01 - Damien Costello 17 this happens because for Prolog to bind the free variables in a subgoal, that subgoal must unify with some other clause and the subgoal must succeed the correct way to handle unbound variables within a not subgoal is with anonymous variables. October, 01 - Damien Costello 18 Damien Costello, Dept of Computing & Maths, GMIT 3

4 Functional & Logic Programming - October, 01 examples of correct clauses and incorrect clauses likes(bill, Anyone):-/* 'Anyone' is output argument */ likes(sue, Anyone), not(hates(bill, Anyone). Anyone is bound by likes(sue, Anyone) before finds out that hates(bill, Anyone) is not true this clause works just as it should October, 01 - Damien Costello 19 rewrite this so that it calls not first get error message - free variables not allowed in not. likes(bill, Anyone):-/* This won't work right */ not(hates(bill, Anyone)), likes(sue, Anyone). even if you correct this (by replacing Anyone in not(hates(bill, Anyone)) with an anonymous variable) will still return the wrong result. October, 01 - Damien Costello 20 likes(bill, Anyone):-/* This won't work right */ not(hates(bill, _)), likes(sue, Anyone). states that Bill likes Anyone if nothing that Bill hates is known and if Sue likes Anyone original clause stated that Bill likes Anyone if there is some Anyone that Sue likes and that Bill does not hate October, 01 - Damien Costello 21 with cut and negation always a catch advantages using cut often improves the efficiency of the program explicitly tell Prolog not to try other alternatives as they will fail using cut can specify mutually exclusive rules if P then Q otherwise R enhancing expressiveness October, 01 - Damien Costello 22 with cut and negation reservations can loose correspondence between the declarative and procedural meaning with no cut - can change the order of the clauses affecting the efficiency or termination of the program with cut - change in order may affect delarative meaning can get different results example to follow October, 01 - Damien Costello 23 p is true if and only if a & b are true or c is true p <=> (a & b) c p :- a,b. p :- c. change the order of the clauses and won t loose meaning however, rewrite with a cut p :- a,!, b. p :- c. p <=> (a & b) ( a & c) now changing the order changes the meaning October, 01 - Damien Costello 24 Damien Costello, Dept of Computing & Maths, GMIT 4

5 Functional & Logic Programming - October, 01 using the cut have to pay more attention to procedural aspects increases the probability of programming error green cuts will not change the declarative meaning when reading a program, can ignore these easier to use red cuts will affect the meaning October, 01 - Damien Costello 25 difficulty with not not human(mary) prolog will probably answer yes not saying that Mary is not human not enough proof to say Mary is human with not prolog tries to prove the opposite if it cannot be proven, then the not is true closed world assumption October, 01 - Damien Costello 26 closed world assumption everything that exists is stated in the program or can be derived from the program consequently, if something is not in the program then it is not true and its negation is true don t normally presume that the world is closed October, 01 - Damien Costello 27 Damien Costello, Dept of Computing & Maths, GMIT 5